NumHask.Data.Complex

Complex numbers.

Documentation

data Complex a

Complex numbers have real and imaginary parts.

The Foldable and Traversable instances traverse the real part first.

Constructors

!a :+ !a infix 6

forms a complex number from its real and imaginary rectangular components.

Instances

Functor Complex

Defined in NumHask.Data.Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Foldable Complex

Defined in NumHask.Data.Complex

Methods

fold :: Monoid m => Complex m -> m

foldMap :: Monoid m => (a -> m) -> Complex a -> m

foldMap' :: Monoid m => (a -> m) -> Complex a -> m

foldr :: (a -> b -> b) -> b -> Complex a -> b

foldr' :: (a -> b -> b) -> b -> Complex a -> b

foldl :: (b -> a -> b) -> b -> Complex a -> b

foldl' :: (b -> a -> b) -> b -> Complex a -> b

foldr1 :: (a -> a -> a) -> Complex a -> a

foldl1 :: (a -> a -> a) -> Complex a -> a

toList :: Complex a -> [a]

null :: Complex a -> Bool

length :: Complex a -> Int

elem :: Eq a => a -> Complex a -> Bool

maximum :: Ord a => Complex a -> a

minimum :: Ord a => Complex a -> a

sum :: Num a => Complex a -> a

product :: Num a => Complex a -> a

Traversable Complex

Defined in NumHask.Data.Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b)

sequenceA :: Applicative f => Complex (f a) -> f (Complex a)

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b)

sequence :: Monad m => Complex (m a) -> m (Complex a)

Eq a => Eq (Complex a)

Defined in NumHask.Data.Complex

Methods

(==) :: Complex a -> Complex a -> Bool

(/=) :: Complex a -> Complex a -> Bool

Data a => Data (Complex a)

Defined in NumHask.Data.Complex

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a)

toConstr :: Complex a -> Constr

dataTypeOf :: Complex a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a))

gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r

gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a)

Read a => Read (Complex a)

Defined in NumHask.Data.Complex

Methods

readsPrec :: Int -> ReadS (Complex a)

readList :: ReadS [Complex a]

readPrec :: ReadPrec (Complex a)

readListPrec :: ReadPrec [Complex a]

Show a => Show (Complex a)

Defined in NumHask.Data.Complex

Methods

showsPrec :: Int -> Complex a -> ShowS

show :: Complex a -> String

showList :: [Complex a] -> ShowS

Generic (Complex a)

Defined in NumHask.Data.Complex

Associated Types

type Rep (Complex a) :: Type -> Type

Methods

from :: Complex a -> Rep (Complex a) x

to :: Rep (Complex a) x -> Complex a

Subtractive a => Subtractive (Complex a)

Defined in NumHask.Data.Complex

Methods

negate :: Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

Additive a => Additive (Complex a)

Defined in NumHask.Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a

zero :: Complex a

(Subtractive a, Divisive a) => Divisive (Complex a)

Defined in NumHask.Data.Complex

Methods

recip :: Complex a -> Complex a

(/) :: Complex a -> Complex a -> Complex a

(Subtractive a, Multiplicative a) => Multiplicative (Complex a)

Defined in NumHask.Data.Complex

Methods

(*) :: Complex a -> Complex a -> Complex a

one :: Complex a

(Distributive a, Subtractive a) => InvolutiveRing (Complex a)

Defined in NumHask.Data.Complex

Methods

adj :: Complex a -> Complex a

(Distributive a, Subtractive a) => Distributive (Complex a)

Defined in NumHask.Data.Complex

LowerBoundedField a => LowerBoundedField (Complex a)

Defined in NumHask.Data.Complex

Methods

negInfinity :: Complex a

(UpperBoundedField a, Subtractive a) => UpperBoundedField (Complex a)

Defined in NumHask.Data.Complex

Methods

infinity :: Complex a

nan :: Complex a

(Ord a, TrigField a, ExpField a) => ExpField (Complex a)

Defined in NumHask.Data.Complex

Methods

exp :: Complex a -> Complex a

log :: Complex a -> Complex a

logBase :: Complex a -> Complex a -> Complex a

(**) :: Complex a -> Complex a -> Complex a

sqrt :: Complex a -> Complex a

Field a => Field (Complex a)

Defined in NumHask.Data.Complex

BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Complex a)

Defined in NumHask.Data.Complex

Methods

top :: Complex a

BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Complex a)

Defined in NumHask.Data.Complex

Methods

bottom :: Complex a

MeetSemiLattice a => MeetSemiLattice (Complex a)

Defined in NumHask.Data.Complex

Methods

(/\) :: Complex a -> Complex a -> Complex a

JoinSemiLattice a => JoinSemiLattice (Complex a)

Defined in NumHask.Data.Complex

Methods

(\/) :: Complex a -> Complex a -> Complex a

(Ord a, Signed a, Subtractive a, Epsilon a) => Epsilon (Complex a)

Defined in NumHask.Data.Complex

Methods

epsilon :: Complex a

nearZero :: Complex a -> Bool

aboutEqual :: Complex a -> Complex a -> Bool

Generic1 Complex

Defined in NumHask.Data.Complex

Associated Types

type Rep1 Complex :: k -> Type

Methods

from1 :: forall (a :: k). Complex a -> Rep1 Complex a

to1 :: forall (a :: k). Rep1 Complex a -> Complex a

(Additive a, FromIntegral a b) => FromIntegral (Complex a) b

Defined in NumHask.Data.Complex

Methods

fromIntegral :: b -> Complex a

TrigField a => Direction (Complex a) a

Defined in NumHask.Data.Complex

Methods

angle :: Complex a -> a

ray :: a -> Complex a

ExpField a => Norm (Complex a) a

A euclidean-style norm is strong convention for Complex.

Defined in NumHask.Data.Complex

Methods

norm :: Complex a -> a

basis :: Complex a -> Complex a

type Rep (Complex a)

Defined in NumHask.Data.Complex

type Rep (Complex a) = D1 ('MetaData "Complex" "NumHask.Data.Complex" "numhask-0.8.1.0-6vtGETGPv6z5KBqA0pprnK" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))

type Rep1 Complex

Defined in NumHask.Data.Complex

type Rep1 Complex = D1 ('MetaData "Complex" "NumHask.Data.Complex" "numhask-0.8.1.0-6vtGETGPv6z5KBqA0pprnK" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

realPart :: Complex a -> a

Extracts the real part of a complex number.

imagPart :: Complex a -> a

Extracts the imaginary part of a complex number.